The discussion centers on the use of swap gates in Quantum Fourier Transform (QFT) circuits, specifically addressing their role in reversing the order of qubits. The QFT's output typically presents qubits in reverse order, transitioning between big-endian and little-endian formats. This swap facilitates a consistent interpretation of the output, aligning it with the conventional definition of the discrete Fourier transform, where F(1) corresponds to the lowest non-zero frequency. The clarification provided indicates that the amplitude of the state 10010 corresponds to the 9/N frequency, correcting an earlier misstatement regarding the 7/N frequency.
PREREQUISITESQuantum computing enthusiasts, researchers in quantum algorithms, and practitioners designing quantum circuits who seek to understand the intricacies of QFT and qubit manipulation.
jimmycricket said:I'm currently working through Nielsen & Chuang's section on the circuit design for implementing the QFT. I'm confused as to why swap gates are used in the model to swap the order of qubits. Heres what I'm looking at http://www.johnboccio.com/research/quantum/notes/QC10th.pdf page 247 figure 5.1
Can anybody help?
Strilanc said:Here's a blog post about the QFT with some puzzles in a circuit simulator.
The basic reason is that the QFT's output has the qubits in the reverse order of what you typically want. It switches you from big-endian bits to little-endian bits (or vice versa), so that the amplitude of the state 10010 corresponds to the 7/N frequency instead of the 18/N frequency (or vice-versa).
You don't have to swap them back into the right order, it just makes it easier to think about the QFT when used as a tool because you're keeping the endian-ness consistent. It makes the result match the usual definition of the discrete Fourier transform, where F(1) corresponds to the lowest non-zero frequency (instead of what F(N-1) corresponds to).
Do you mean the 9/N frequency not 7/N. Am I right in saying the qubits in your example reversed would read 01001=9?Strilanc said:Here's a blog post about the QFT with some puzzles in a circuit simulator.
The basic reason is that the QFT's output has the qubits in the reverse order of what you typically want. It switches you from big-endian bits to little-endian bits (or vice versa), so that the amplitude of the state 10010 corresponds to the 7/N frequency instead of the 18/N frequency (or vice-versa).
jimmycricket said:Do you mean the 9/N frequency not 7/N. Am I right in saying the qubits in your example reversed would read 01001=9?